Find the value of curvature of a curve where α is maximum

Question

Consider the regular curve α(t) = (t, t²-4t-3), t ∈ R. For what value of t is the curvature of α maximum?

Answer 1

The curvature function is $k(t)=\frac{x'y''-x''y'}{((x')^2+(y')^2){\frac{3}{2}}}=\frac{2}{(4(t-2)^2+1)^{\frac{3}{2}}}$.

Maimum curvature is $k=2$ at $t=2$ which occured at the vertex of parabola. I didn't know that!